This invention relates to a variable impedance circuit capable of electrically increasing or decreasing the impedance, such as resistance and capacitance.
Recently, the function of semiconductor integrated circuits has been greatly improved, and the filter circuit has come to be incorporated in a semiconductor chip as an integrated circuit. Generally a filter circuit is composed of a resistance element and a capacitance element. To change the filtering characteristic of the filter circuit, it is necessary to vary the value of constituent elements, that is, the capacitance element or the resistance element. Accordingly, hitherto, a variable impedance circuit has been used, which can vary the value of capacitance element or resistance element built in a semiconductor chip.
FIG. 12 shows a conventional variable capacitance circuit used for such a purpose, expressed only by an AC circuit. In FIG. 13, the variable capacitance circuit in FIG. 12 is expressed by both an AC circuit and DC circuit.
In FIG. 12 and FIG. 13, a differential amplifier circuit 15 is composed of transistors Q.sub.5, Q.sub.6, and a resistance element 10 connected between their emitters. A differential amplifier circuit 16 is composed of transistors Q.sub.7, Q.sub.8, and a resistance element 11 connected between their emitters. A differential amplifier circuit 17 is composed of transistors Q.sub.1, Q.sub.2, and a resistance element 12 connected between their emitters. A differential amplifier circuit 18 is composed of transistors Q.sub.3, Q.sub.4, and a resistance element 13 connected between their emitters. As is clear from FIG. 12 and FIG. 13, the differential amplifier circuits 15, 16 are so connected that the input terminals of one differential amplifier circuit are connected to the output terminals of the other differential amplifier circuit. The differential amplifier circuits 17, 18 are also connected in a similar relation. These differential amplifier circuits 15, 16, 17 and 18 are connected as shown in FIG. 12, FIG. 13, and a capacitance element 14 is connected between two output terminals of the differential amplifier circuit 17. The transistors Q.sub.1 to Q.sub.8 for composing the differential amplifier circuits 15, 16, 17 and 18 are supplied with biases from voltage sources V.sub.0, V.sub.1, and constant current source I.sub.0 as shown in FIG. 13.
The voltage-current conversion factors of the differential amplifier circuits 15, 16, 17 and 18 are determined respectively by the characteristics of the resistance elements 10, 11, 12 and 13.
The operation is explained below.
The relation EQU i.sub.2 =g.sub.1 .multidot.V.sub.1 ( 1)
is established between voltage V.sub.1 and output current i.sub.2 across input terminals of the differential amplifier circuit 17. In this equation g.sub.1 denotes the voltage-current conversion factor of the differential amplifier circuit 17, and supposing the emitter resistance value of transistors Q.sub.1, Q.sub.2 to be r.sub.el, and the value of resistance element 12 between emitters to be R.sub.1, g.sub.1 it is expressed as follows. ##EQU1##
The characteristics of voltage V.sub.2 and current i.sub.2 occurring at both ends of the capacitance element 14 of capacitance value C.sub.0 are obtained as follows. EQU i.sub.2 =-j.omega.C.sub.0 .multidot.V.sub.2 ( 3)
Similarly, the characteristics of voltage V.sub.2 across input terminals and output current i.sub.1 of the differential amplifier circuit 18 composed of transistors Q.sub.3, Q.sub.4 are obtained as follows: EQU i.sub.1 =-g.sub.2 .multidot.V.sub.2 ( 4)
where g.sub.2 denotes the voltage-current conversion factor of the differential amplifier circuit 18, and supposing the resistance value of each emitter of transistors Q.sub.3, Q.sub.4 to be r.sub.e2, and the value of the resistance element 13 between the emitters to be R.sub.2, g.sub.2 is expressed as follows. ##EQU2##
Solving V.sub.1 and i.sub.1 from equations (1), (3) and (4), it is known from equations (1), (3) that ##EQU3## and from equations (4), (6) that ##EQU4##
That is, ##EQU5##
Here, the inductance L is given as follows. ##EQU6##
Furthermore, from equations (2), (5), it follows that EQU L=(R.sub.1 +2r.sub.el)(R.sub.2 +2r.sub.e2)C.sub.0 ( 10)
Usually, the resistance values can be set so as to establish the relation of R.sub.1 &gt;r.sub.el, R.sub.2 &gt;r.sub.e2, and hence the inductance L can be approximated as EQU L=R.sub.1 .multidot.R.sub.2 .multidot.C.sub.0
Likewise, the characteristics of input terminal voltage V.sub.3 and output current i.sub.4 of the differential amplifier circuit 15 composed of transistors Q.sub.5, Q.sub.6 may be expressed as follows, supposing the voltage-current conversion factor of the differential amplifier circuit 15 to be g.sub.3 : EQU i.sub.4 =g.sub.3 .multidot.V.sub.3 ( 11)
Supposing the voltage-current conversion factor of the differential amplifier circuit 16 to be g.sub.4, the characteristics of input terminal voltage V.sub.4 and output current i.sub.3 of the differential amplifier 16 composed of transistors Q.sub.7, Q.sub.8 are as follows. EQU i.sub.3 =-g.sub.4 .multidot.V.sub.4 ( 12)
The circuit systems respectively composed of the differential amplifier circuits 15, 16, and the differential amplifier circuits 17, 18 represent the conventionally used phase conversion circuits. The circuit system composed of the differential amplifiers 17, 18 is designed to apply from capacitance characteristics to inductance characteristics, in terms of circuitry.
In FIG. 12 and FIG. 13, the relations EQU V.sub.4 =V.sub.1 ( 13) EQU i.sub.4 =-i.sub.1 ( 14)
are established between the voltages V.sub.1, V.sub.4, and currents i.sub.4, i.sub.1, respectively. Hence, equation (8) is rewritten as ##EQU7## and further by eliminating i.sub.4 from equation (11), it results in ##EQU8## and from equations (16) and (12), it follows that ##EQU9##
The capacitance value C applied between the voltage V.sub.3 and current i.sub.3 is given as ##EQU10## That is, by properly selecting the values for the voltage-current conversion factors g.sub.1, g.sub.2, g.sub.3 and g.sub.4, the capacity value C is newly created electrically.
However, in the conventional variable capacitance circuit shown in FIG. 12, FIG. 13, at least four differential amplifier circuits are needed in order to obtain a new capacitance value by electrically increasing or decreasing the capacitance. Accordingly, the circuit composition is complicated, the number of required elements increases, and the chip area increases.
A conventional variable resistance circuit incorporated in a semiconductor chip is explained below while referring to FIG. 14.
In FIG. 14, transistors 41, 42 are connected between a constant voltage source 40 and the grounding potential. A constant voltage source 43 is connected to the base of the transistor 41. A variable voltage source 44 is connected to the base of the transistor 42. An output terminal 45 is connected to the connecting points of the transistors 41, 42.
In the structure in FIG. 14, the resistance value as seen from the output terminal 45 is equal to the differential emitter resistance of the transistor 41 (that is, the impedance of the transistor 41 seen from its emitter), and it is given in the following formula. ##EQU11## where k is Boltzmann constant, T is absolute temperature, q is electric charge quantity of an electron, and I.sub.0 is emitter current flowing in the transistor 41. When the voltage of the variable voltage source 44 is varied, the current I.sub.0 changes, and hence the resistance value as seen from the output terminal 45 varies. Therefore, by controlling the voltage of the variable voltage source 44, a variable resistance may be obtained.
However, in the conventional variable resistance circuit shown in FIG. 14, since the differential emitter resistance itself of the transistor 41 is used as a variable resistance component, the variable range of the resistance value is narrow.